0,2

7*a(n)^2 - 5*b(n)^2 = 2 with companion sequence b(n)=A077416(n), n>=0.

a(n) = L(n,12), where L is defined as in A108299; see also A077416 for L(n,-12). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 01 2005

[a(n), A004191(n)] = the 2 X 2 matrix [1,10; 1,11]^(n+1) * [1,0]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 19 2008

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = 12*a(n-1) - a(n-2), a(-1)=1, a(0)=1.

a(n) = S(n, 12) - S(n-1, 12) = T(2*n+1, sqrt(14)/2)/(sqrt(14)/2) with S(n, x) := U(n, x/2), resp. T(n, x), Chebyshev's polynomials of the second, resp. first, kind. See A049310 and A053120. S(-1, x)=0, S(n, 12)=A004191(n).

G.f.:(1-x)/(1-12*x+x^2).

a(n) = (ap^(2*n+1) + am^(2*n+1))/sqrt(14) with ap := (sqrt(7)+sqrt(5))/sqrt(2) and am := (sqrt(7)-sqrt(5))/sqrt(2).

a(n) = sqrt((5*A077416(n)^2 + 2)/7).

a(n)a(n+3) = 120 + a(n+1)a(n+2). - R. Stephan, May 29 2004

Cf. A072256(n) with companion A054320(n-1), n>=1.

Row 12 of array A094954.

Cf. A004191.

Adjacent sequences: A077414 A077415 A077416 this_sequence A077418 A077419 A077420

Sequence in context: A076255 A076357 A015606 this_sequence A082148 A075509 A061113

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002